Organizing the Global Value Chain Pol Antr` as Davin Chor Harvard - - PowerPoint PPT Presentation

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence

Organizing the Global Value Chain

Pol Antr` as Davin Chor Harvard SMU 9-12 July 2012 NBER SI

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence

Motivation and Introduction

Many production processes are sequential in nature:

◮ Raw materials processing −

→ Basic components − → Complex assembly − → Sales and Distribution

◮ Downstream stages often cannot commence before upstream stages ◮ Classic motivating example: Henry Ford’s Model T production line ◮ More recently: Sequential production processes now often fragmented

across country borders

◮ Existing literature: On the consequences of sequential location decisions

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence

Motivation and Introduction

Many production processes are sequential in nature:

◮ Raw materials processing −

→ Basic components − → Complex assembly − → Sales and Distribution

◮ Downstream stages often cannot commence before upstream stages ◮ Classic motivating example: Henry Ford’s Model T production line ◮ More recently: Sequential production processes now often fragmented

across country borders

◮ Existing literature: On the consequences of sequential location decisions ◮ This paper: What is the optimal way to organize production along such

global sequential production processes?

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence

Motivation and Introduction

Our premise: Contractual frictions matter for the organizational decisions of firms over particular production stages

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence

Motivation and Introduction

Our premise: Contractual frictions matter for the organizational decisions of firms over particular production stages Example: The Boeing Dreamliner

◮ Repeated delays led to reorganization of the sourcing model ◮ In 2008-09, Boeing successively acquired Vought Aircraft Industries’

• perations in South Carolina, which were producing rear sections of the

Dreamliner’s fuselage

◮ Culminated in a full buyout in Jul 2009:

“The 787’s entry into service has been set back five times, in part because multiple suppliers didn’t do all the work they had agreed to, leaving more for Boeing workers to complete.”

Source: http://www.bloomberg.com/apps/news?pid=newsarchive&sid=aF6uWvMb9C08 Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence

Some Questions

◮ Why does the firm not bring the whole production process within its firm

boundaries?

◮ What determines which suppliers are brought inside the firm and which are

not, and why might “downstreamness” matter for this?

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence

Some Questions

◮ Why does the firm not bring the whole production process within its firm

boundaries?

◮ What determines which suppliers are brought inside the firm and which are

not, and why might “downstreamness” matter for this?

◮ Property-rights theory (Grossman and Hart, 1986, Hart and Moore, 1990)

provides the most convincing framework to answer the first question...

◮ ... so it seems a natural approach to use to tackle the second question as

well

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence

What We Do

Analyze the organizational decision along sequential production lines:

◮ Develop a model of firm production with a continuum of uniquely

sequenced production stages

◮ In each stage: Firm contracts with a distinct supplier for a stage-specific

input that needs to be made compatible with all other stage inputs

◮ In an incomplete contracts setting, obtain a sharp characterization of the

• ptimal ownership structure along the value chain

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence

What We Do

Analyze the organizational decision along sequential production lines:

◮ Develop a model of firm production with a continuum of uniquely

sequenced production stages

◮ In each stage: Firm contracts with a distinct supplier for a stage-specific

input that needs to be made compatible with all other stage inputs

◮ In an incomplete contracts setting, obtain a sharp characterization of the

• ptimal ownership structure along the value chain

◮ Empirically, test predictions of the model using:

(i) the intrafirm trade share (to capture the prevalence of integration); (ii) novel measures of the downstreamness of particular inputs (which we develop from Input-Output Tables)

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence

Related Literature

• 1. Sequential production

◮ Eg: Findlay (1978), Dixit and Grossman (1982), Sanyal (1983), Kremer

(1993), Yi (2003), Harms, Lorz, and Urban (2009), Baldwin and Venables (2010), Costinot et al. (2011)

◮ Small literature on incentives in sequential production processes. Eg:

Winter (2006), Kim and Shin (2011)

• 2. Property rights theory of the firm in international trade

◮ Eg: Grossman and Helpman (2002, 2005), Antr`

as (2003), Antr` as and Helpman (2004, 2008)

• 3. Empirical evidence (determinants of the intrafirm trade share)

◮ Eg: Antr`

as (2003), Tomiura (2007), Defever and Toubal (2007), Nunn and Trefler (2008a,b), Corcos et al. (2009), D´ ıez (2010), Bernard et al. (2010), Kohler and Smolka (2010)

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Plan of Talk

• 1. Motivation and Introduction
• 2. Setup of the Core Model
• 3. Key Predictions
• 4. Extensions
• 5. Empirical Evidence
• 6. Conclusion

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Basic Setup: Production Function

◮ Production requires the completion of a continuum of stages indexed by

j ∈ [0, 1]

◮ Unique sequence of stages: j increasing as production moves downstream ◮ Let x(j) be the services of compatible intermediate inputs that supplier j

delivers to the Firm. Quality-adjusted volume of final-good production is q = θ 1 x(j)αI (j) dj 1/α , (1) I (j) = 1 if input j is produced after all inputs j′ < j

• therwise

◮ α ∈ (0, 1): captures how substitutable the stage inputs are ◮ θ: firm productivity parameter

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Basic Setup: Production Function (cont.)

Short remark:

◮ Alternative recursive representation of technology in (1):

q′ (m) = 1 αθαx(m)αq (m)1−α I (m)

◮ Change in quality-adjusted output brought about by supplier at stage m is

Cobb-Douglas in input m and q(m)

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Basic Setup: Supply of inputs

◮ Each intermediate input needs to be produced by a different supplier ◮ Suppliers need to undertake a relationship-specific investment to produce a

compatible input

◮ One unit of investment generates one unit of x(j), the services of the

stage j compatible input

◮ Marginal cost of investment is common for all suppliers and equal to c

(although this can be relaxed)

◮ Incompatible inputs can be produced by all agents (including the Firm) at

a negligible marginal cost, but they add no value to final-good production (other than allowing completion)

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Basic Setup: Final good demand

◮ Consumers have preferences:

U =

• ω∈Ω

(ϕ (ω) ˜ q (ω))ρ dω 1/ρ , with ρ ∈ (0, 1) (2)

◮ ϕ (ω): quality of a variety ◮ ˜

q (ω): consumption in physical units

◮ Implied revenue function of any firm in the industry is concave in

quality-adjusted output q (ω) = ϕ (ω) ˜ q (ω) with a constant elasticity ρ: r = A1−ρqρ = A1−ρθρ 1 x (j)α dj ρ/α (3)

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Some Key Features

Value generated up to stage m if all inputs are compatible: r(m) = A1−ρθρ m x(j)α dj ρ

α

(4) Incremental value generated at stage m by producing a compatible input: r ′(m) = ∂r (m) ∂m = ρ α

• A1−ρθρ α

ρ [r(m)] ρ−α ρ

x(m)α (5) Key consideration: How does the value of production up to stage m affect the marginal contribution of supplier m?

◮ If ρ > α, the effect is positive (sequential complements case) ◮ If ρ < α, the effect is negative (sequential substitutes case)

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Some Key Features (cont.)

Why does ρ matter?

◮ From a technological point of view, all inputs are complements since

α ∈ (0, 1)

◮ But when ρ is small, firm faces an inelastic demand function, so marginal

revenue falls quickly with quality-adjusted output

◮ Large investments prior to stage m therefore discourage supplier effort at

stage m

◮ It turns out that when ρ < α, this revenue effect is strong enough to

dominate the physical input complementarity effect

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Benchmark: Complete Contracts

If contracting frictions are absent, firm signs a contract with each input supplier specifying the optimal quantity of compatible inputs, x(j), to maximize: πF = A1−ρθρ 1 x(j)αdj ρ

α

− c 1 x(j)dj (6) Solution entails:

◮ A common investment level, x =

• ρA1−ρθρ/c

1/(1−ρ), for all inputs j

◮ Suppliers are paid their marginal cost: cx ◮ Even though

r ′(m) = ∂r (m) ∂m = ρ α

• A1−ρθρ α

ρ [r(m)] ρ−α ρ

x(m)α, the Firm internalizes the downstream effects of upstream investments

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Incomplete Contracting

Suppose that the environment is one of incomplete contracts

◮ Compatibility cannot be verified and enforced by a third-party court ◮ But Firm and suppliers have symmetric information regarding compatibility ◮ Contracts contingent on total revenue are not useful in our context ◮ Abstract from mechanisms ◮ Suppliers’ payoffs are determined in ex post (re)-negotiation, after x(m)

has been produced

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Bargaining

◮ Supplier m and Firm engage in generalized Nash bargaining over the

incremental value contribution made by supplier m, r ′(m)

◮ Supplier m’s outside option normalized to 0 ◮ Under integration, Firm’s control rights tilt the ex-post division of surplus

in its favor relative to under outsourcing (as in Grossman and Hart, 1986).

◮ Let β (m) be the share of r ′(m) that accrues to the firm in the bargain:

β (m) =    βO if the firm outsources stage m βV > βO if the firm integrates stage m

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Timing

• 1. Firm posts contracts for suppliers for each stage j ∈ [0, 1], stating the
• rganizational mode (integration vs outsourcing).
• 2. Suppliers apply. Firm chooses one supplier for each stage j.
• 3. Production takes place sequentially. The supplier chooses x(m) after
• bserving the value of r(m).
• 4. At the end of stage m, the supplier and Firm bargain over r ′(m). Firm

pays the supplier.

• 5. Total revenue, A1−ρqρ, ρ ∈ (0, 1), from the sale of the final good is

collected by the Firm.

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Discussion

◮ Bargaining is over supplier’s marginal contribution at stage m, not its

ultimate (or average marginal) contribution

◮ Can be rationalized by limited commitment frictions: Hart and Moore

(1994), Thomas and Worrall (1994)

◮ Supplier does not want to delay receiving payment; or Firm might be

constrained in borrowing more than r ′(m)

◮ Note: Results surprisingly robust to alternative bargaining protocols

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Plan of Talk

• 1. Motivation and Introduction
• 2. Setup of the Core Model
• 3. Key Predictions
• 4. Extensions
• 5. Empirical Evidence
• 6. Conclusion

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Key Tradeoffs

◮ Ownership confers a higher fallback option to the firm and allows it to

extract more surplus

◮ But foreseeing a lower return to their investments, integrated suppliers will

under-invest relatively more, ie choose a lower x(m): max

x(m)

(1 − β (m)) r ′(m) − cx(m) (7)

◮ Downstream effect: on the incentives to invest of all suppliers that are

positioned downstream relative to the supplier being integrated

◮ This downstream effect is negative in the complements case, but it is

positive in the substitutes case

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Supplier Behavior Along the Value Chain

Plug the expression for x(m) to obtain a differential equation in r(m): r ′(m) = ρ α (1 − β (m)) ρθ c

• α

1−α

A

α(1−ρ) ρ(1−α) (r(m)) ρ−α ρ(1−α)

Solving this yields revenues up to stage m as a function of model parameters and in particular, the β(j)’s for j < m: r(m) = A 1 − ρ 1 − α ρ(1−α)

α(1−ρ) ρθ

c

• ρ

1−ρ m

j=0

(1 − β(j))

α 1−α dj

ρ(1−α)

α(1−ρ)

(8) Then, solve for the overall profits of the firm by integrating over stages: ΠS = 1

j=0

β(j)r ′ (j) dj

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

The Make-or-Buy Decision

Before production begins, firm chooses β(j) ∈ {βV , βO} for j ∈ [0, 1] to maximize ΠS

Proposition

In the complements case (ρ > α), there exists a unique m∗

C ∈ (0, 1], such that:

(i) all production stages m ∈ [0, m∗

C) are outsourced; and (ii) all stages

m ∈ [m∗

C, 1] are integrated within firm boundaries.

In the substitutes case (ρ < α), there exists a unique m∗

S ∈ (0, 1], such that: (i)

all production stages m ∈ [0, m∗

S) are integrated within firm boundaries; and

(ii) all stages m ∈ [m∗

S, 1] are outsourced.

Proof

Remark: m∗

C and m∗ S can be solved for in closed-form

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

The Make-or-Buy Decision (cont.)

Additional predictions:

Proposition

Whenever integration and outsourcing coexist along the value chain, i.e., m∗

C ∈ (0, 1) when ρ > α or m∗ S ∈ (0, 1) when ρ < α, a decrease in ρ will

necessarily expand the range of stages that are vertically integrated. Intuition:

◮ When ρ is low, firm has high market power, and hence will focus on the

rent extraction motive for integration

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Plan of Talk

• 1. Motivation and Introduction
• 2. Setup of the Core Model
• 3. Key Predictions
• 4. Extensions
• 5. Empirical Evidence
• 6. Conclusion

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Extensions

Benchmark model can be readily extended to connect it to the global sourcing framework in Antr` as and Helpman (2004) by adding:

• 1. Headquarter intensity
• 2. Firm heterogeneity
• 3. Supplier heterogeneity

Extensions are important for helping us to map the theoretical predictions to the empirics

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Setup of the Model Key Predictions Extensions

Summary of Extensions

• 1. Headquarter intensity:

Extension 1 ◮ Introduce Firm investment in headquarter services prior to stage 0; fully

non-contractible

◮ Obtain: integration more prevalent in headquarter intensive sectors ◮ Otherwise: Similar to core model, but with ρ replaced by ˜

ρ ≡ (1 − η)ρ

• 2. Firm heterogeneity:

Extension 2 ◮ θ’s drawn from Pareto distribution; introduce fixed organizational costs ◮ Converts previous within-firm results into predictions on the relative

prevalence of integration at the industry level

• 3. Supplier heterogeneity:

Extension 3 ◮ Results generalize, but it might be important to control for unobserved

country cost differences and for selection

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Plan of Talk

• 1. Motivation and Introduction
• 2. Setup of the Core Model
• 3. Key Predictions
• 4. Extensions
• 5. Empirical Evidence
• 6. Conclusion

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Empirical specification

Sit = β1Di × 1(ρi < ρmed) + β2Di × 1(ρi > ρmed) + β31(ρi > ρmed) +βXXi + αt + εit

◮ Sit: share of intrafirm trade in U.S. imports for industry i, year t

◮ Data source: U.S. Census Bureau Related Party Database ◮ 253 manufacturing industries, 11 years (2000-2010)

◮ Di: “downstreamness” of an industry ◮ 1(ρi ≷ ρmed): indicator for complements vs substitutes case

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Empirical specification

Sit = β1Di × 1(ρi < ρmed) + β2Di × 1(ρi > ρmed) + β31(ρi > ρmed) +βXXi + αt + εit

◮ Sit: share of intrafirm trade in U.S. imports for industry i, year t

◮ Data source: U.S. Census Bureau Related Party Database ◮ 253 manufacturing industries, 11 years (2000-2010)

◮ Di: “downstreamness” of an industry ◮ 1(ρi ≷ ρmed): indicator for complements vs substitutes case ◮ Xi: other industry controls ◮ αt: year fixed effects (in country-industry-year specifications, include

country-year fixed effects, αct, instead)

◮ Cluster standard errors by industry

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Measuring downstreamness: Preliminaries

Start with the output identity for industry i in a closed-economy: Yi = Fi +

• j

dijYj = Fi +

• j

dijFj

• direct use of i as input

+

• j
• k

dikdkjFj +

• j
• k
• l

dildlkdkjFj + . . .

• indirect use of i as input

In compact matrix form: Y = F + DF + D2F + D3F + D4F + . . . = [I − D]−1 F. where D is the N × N matrix of direct requirement coefficients; F is the N × 1 matrix of final use values (going to consumption and investment)

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Measures of downstreamness 1

Constructed from 2002 U.S. Input-Output Use Tables:

◮ DUse TUsei: Ratio of aggregate direct use to aggregate total use of i as

an input in the production of final goods

◮ Direct Use =

j dijFj

◮ Total Use =

j dijFj + j

• k dikdkjFj +

j

• k
• l dildlkdkjFj + . . .

Interpretation: Higher DUse TUsei implies larger share of input i is used directly rather than entering indirectly earlier in the production process Consistent with input being used further downstream on average Computation: i-th entry of DF divided by i-th entry of Y − F

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Measures of downstreamness 2

◮ Start with:

Ui = 1 · Fi Yi + 2 · N

j=1 dijFj

Yi + 3 · N

j=1

N

k=1 dikdkjFj

Yi +4 · N

j=1

N

k=1

N

l=1 dildlkdkjFj

Yi + ... Interpretation: Take a weighted average distance from final use, where the weights are the industry’s use value at each stage (normalized by Yi) Computation: i-th entry of [I − D]−2F divided by i-th entry of Y See Antr` as, Chor, Fally, and Hillberry (AER P&P 2012) for more

◮ Ui ≥ 1: Reciprocate to get DownMeasurei, increasing in downstreamness

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Measures of downstreamness 2

Remarks:

◮ ACFH (2012) show that Ui is equivalent to a recursively-defined measure

• f distance from final use in Fally (2012)

◮ Also equivalent to a measure of cost-push effects or total “forward

linkages” in supply-side I-O analysis Ui is equal to the dollar amount by which output of all sectors increases following a $1 increase in value-added in sector i

◮ Empirical implementation: ACFH (2012) show how to apply an

• pen-economy adjustment to D and F as reported in I-O Tables, to

account for net exports and net change in inventories

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Measures of downstreamness (cont.)

IO2002 Industry DUse_TUse IO2002 Industry DownMeasure 331314 Secondary smelting and alloying of aluminum 0.0000 325110 Petrochemical 0.2150 325110 Petrochemical 0.0599 331411 Primary smelting and refining of copper 0.2296 331411 Primary smelting and refining of copper 0.0741 331314 Secondary smelting and alloying of aluminum 0.2461 325211 Plastics material and resin 0.1205 325190 Other basic organic chemical 0.2595 325910 Printing ink 0.1325 33131A Alumina refining and primary aluminum 0.2622 311119 Other animal food 0.1385 325310 Fertilizer 0.2658 333220 Plastics and rubber industry machinery 0.1420 335991 Carbon and graphite product 0.2668 33131A Alumina refining and primary aluminum 0.1447 325181 Alkalies and chlorine 0.2769 335991 Carbon and graphite product 0.1615 331420 Copper rolling, drawing, extruding, and alloying 0.2769 331420 Copper rolling, drawing, extruding, and alloying 0.1804 325211 Plastics material and resin 0.2800 334517 Irradiation apparatus 0.9669 339930 Doll, Toy, and Game 0.9705 339930 Doll, Toy, and Game 0.9686 311111 Dog and cat food 0.9717 337910 Mattress 0.9779 337910 Mattress 0.9720 322291 Sanitary paper product 0.9790 315230 Women's and girl's cut and sew apparel 0.9762 337121 Upholstered household furniture 0.9864 321991 Manufactured home (mobile home) 0.9810 337212 Office furniture and custom woodwork & millwork 0.9868 336212 Truck trailer 0.9837 336213 Motor home 0.9879 336213 Motor home 0.9879 33299A Ammunition 0.9956 316200 Footwear 0.9927 316200 Footwear 0.9967 337121 Upholstered household furniture 0.9928 336111 Automobile 0.9997 336111 Automobile 0.9997 Highest 10 values Lowest 10 values Lowest 10 values Highest 10 values Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Measure of ρi

Constructed from Broda and Weinstein’s (2006) estimates of U.S. import demand elasticities for HS10 products:

◮ Convert to IO2002 categories using HS-IO concordance ◮ ρi is the average elasticity taken over all “buying” industries, i.e. industries

that use i as an input, weighted by the value of input i use in the 2002 Input-Output Tables (Final-use value is included in this calculation; assign it the elasticity of industry i itself)

◮ Baseline specification uses a median value cutoff:

◮ 1(ρi > ρmed): complements case ◮ 1(ρi < ρmed): substitutes case Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Other industry variables

◮ HQ intensity: log(s/l), log(k/l), log(m/l) from NBER-CES

Manufacturing Database

◮ 2000-2005 averages ◮ Also: consider a breakdown of log(k/l) into log(equipment k/l) and

log(plant k/l), in the spirit of Nunn and Trefler (2008b)

◮ R&D intensity: log(R&D/Sales) from Orbis, from Nunn and Trefler

(2008b)

◮ Dispersion: log sd of U.S. exports across ports and destinations (Nunn and

Trefler 2008a)

◮ Distinguish between industry variables constructed for the:

◮ input “selling” industry ◮ input “buying” industry (more consistent with our model) Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Preliminary Evidence: Downstreamness and the Intrafirm Trade Share

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Evidence: DUse TUsei

◮ Greater propensity to integrate downstream in complements case; to outsource

downstream in substitutes case

(1) (2) (3) (4) (5) (6) (7) (8) Elas < Median Elas >= Median Weighted Weighted Log (s/l) 0.005 0.039 0.056 0.112* 0.038

• 0.098

0.005

• 0.068

[0.044] [0.043] [0.042] [0.064] [0.055] [0.079] [0.020] [0.076] Log (k/l) 0.044 0.034 [0.029] [0.027] Log (equipment k / l) 0.085** 0.022 0.153*** 0.188*** 0.026 0.134*** [0.034] [0.047] [0.043] [0.061] [0.016] [0.051] Log (plant k / l)

• 0.077*
• 0.011
• 0.159**
• 0.151**
• 0.056***
• 0.142***

[0.045] [0.057] [0.064] [0.070] [0.019] [0.050] Log (materials/l) 0.058* 0.060* 0.065* 0.049 0.072 0.060 0.025* 0.080 [0.035] [0.034] [0.033] [0.049] [0.047] [0.058] [0.014] [0.049] Log (0.001+ R&D/Sales) 0.055*** 0.054*** 0.053*** 0.050*** 0.054*** 0.090*** 0.031*** 0.073*** [0.009] [0.009] [0.009] [0.013] [0.013] [0.018] [0.004] [0.016] Dispersion 0.081 0.061 0.103 0.034 0.188* 0.160 0.108*** 0.083 [0.070] [0.070] [0.075] [0.108] [0.100] [0.124] [0.038] [0.108] DUse_TUse

• 0.018
• 0.216***

0.225*** [0.054] [0.075] [0.069] DUse_TUse X 1(Elas < Median)

• 0.196***
• 0.174**
• 0.166*
• 0.115***
• 0.075

[0.071] [0.072] [0.089] [0.033] [0.073] DUse_TUse X 1(Elas > Median) 0.171** 0.198*** 0.482***

• 0.035

0.352*** [0.067] [0.068] [0.123] [0.030] [0.118] 1(Elas > Median)

• 0.191***
• 0.191***
• 0.410***
• 0.049*
• 0.291***

[0.062] [0.061] [0.085] [0.029] [0.075] Industry controls for: Buyer Buyer Buyer Buyer Buyer Buyer Buyer Buyer Year fixed effects? Yes Yes Yes Yes Yes Yes No No Country-Year fixed effects? No No No No No No Yes Yes Observations 2783 2783 2783 1375 1408 2783 207991 207991 R-squared 0.27 0.32 0.33 0.37 0.28 0.61 0.18 0.59

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Evidence: DownMeasurei

◮ Similarly strong evidence particularly for the complements case

(1) (2) (3) (4) (5) (6) (7) (8) Elas < Median Elas >= Median Weighted Weighted Log (s/l)

• 0.011

0.019 0.037 0.088 0.032

• 0.143**

0.000

• 0.097*

[0.045] [0.042] [0.041] [0.067] [0.051] [0.058] [0.020] [0.054] Log (k/l) 0.062** 0.058** [0.027] [0.026] Log (equipment k / l) 0.125*** 0.061 0.192*** 0.157** 0.039** 0.139*** [0.036] [0.047] [0.048] [0.066] [0.017] [0.047] Log (plant k / l)

• 0.100**
• 0.027
• 0.192***
• 0.091
• 0.062***
• 0.117**

[0.049] [0.061] [0.073] [0.080] [0.020] [0.052] Log (materials/l) 0.050 0.043 0.049 0.022 0.064 0.032 0.017 0.046 [0.033] [0.033] [0.032] [0.050] [0.043] [0.055] [0.014] [0.043] Log (0.001+ R&D/Sales) 0.058*** 0.054*** 0.054*** 0.053*** 0.050*** 0.089*** 0.032*** 0.072*** [0.010] [0.009] [0.009] [0.014] [0.014] [0.017] [0.004] [0.014] Dispersion 0.087 0.092 0.150* 0.082 0.258** 0.249* 0.116*** 0.163 [0.072] [0.076] [0.079] [0.114] [0.105] [0.147] [0.043] [0.114] DownMeasure 0.101*

• 0.036

0.342*** [0.055] [0.069] [0.081] DownMeasure X 1(Elas < Median)

• 0.024

0.025

• 0.119
• 0.002
• 0.002

[0.064] [0.065] [0.107] [0.035] [0.091] DownMeasure X 1(Elas > Median) 0.249*** 0.298*** 0.526***

• 0.039

0.440*** [0.085] [0.081] [0.100] [0.033] [0.089] 1(Elas > Median)

• 0.115*
• 0.110*
• 0.386***

0.022

• 0.279***

[0.064] [0.062] [0.081] [0.030] [0.072] Industry controls for: Buyer Buyer Buyer Buyer Buyer Buyer Buyer Buyer Year fixed effects? Yes Yes Yes Yes Yes Yes No No Country-Year fixed effects? No No No No No No Yes Yes Observations 2783 2783 2783 1375 1408 2783 207991 207991 R-squared 0.28 0.31 0.33 0.33 0.33 0.64 0.18 0.61

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Evidence: Production Line Position and the Boundaries of the Firm

◮ Results evident with a more flexible quintile treatment of ρi (1) (2) (3) (4) (5) (6) Downstreamness:

DUse_TUse DUse_TUse DUse_TUse DownMeasure DownMeasure DownMeasure Weighted Weighted Weighted Weighted

Downstream X 1(Elas Quintile 1)

• 0.165*
• 0.252*
• 0.138

0.049

• 0.283
• 0.089

[0.093] [0.148] [0.100] [0.119] [0.202] [0.142] Downstream X 1(Elas Quintile 2)

• 0.173
• 0.100
• 0.037
• 0.042
• 0.154
• 0.040

[0.108] [0.136] [0.115] [0.099] [0.139] [0.122] Downstream X 1(Elas Quintile 3)

• 0.145

0.008 0.051 0.019 0.114 0.224 [0.130] [0.166] [0.153] [0.124] [0.166] [0.172] Downstream X 1(Elas Quintile 4) 0.215** 0.159 0.066 0.332*** 0.066 0.073 [0.100] [0.142] [0.119] [0.126] [0.174] [0.120] Downstream X 1(Elas Quintile 5) 0.198* 0.781*** 0.637*** 0.312** 0.736*** 0.621*** [0.103] [0.194] [0.199] [0.130] [0.110] [0.096] Industry controls for: Buyer Buyer Buyer Buyer Buyer Buyer Elas Quintile dummies? Yes Yes Yes Yes Yes Yes Year fixed effects Yes Yes No Yes Yes No Country-Year fixed effects No No Yes No No Yes Observations 2783 2783 207991 2783 2783 207991 R-squared 0.34 0.64 0.61 0.34 0.67 0.62

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Robustness Tests

◮ Robust to controlling for: (i) value-added share; (ii) input “importance”; (iii)

contractibility (Nunn and Trefler 2008); (iv) intermediation (Bernard et al. 2010)

(1) (2) (3) (4) (5) DUse_TUse X 1(Elas < Median)

• 0.187**
• 0.177**
• 0.103
• 0.180**
• 0.130*

[0.074] [0.072] [0.071] [0.077] [0.079] DUse_TUse X 1(Elas > Median) 0.157** 0.198*** 0.236*** 0.159** 0.158** [0.077] [0.068] [0.065] [0.068] [0.074] Value-added / Value shipments 0.187 0.216* [0.135] [0.125] Input "Importance"

• 1.687
• 1.453

[1.231] [1.302] Intermediation

• 0.464***
• 0.413***

[0.106] [0.102] Own Contractibility 0.019 0.024 [0.048] [0.047] Buyer contractibility

• 0.199***
• 0.169**

[0.067] [0.065] Year fixed effects? Yes Yes Yes Yes Yes Observations 2783 2783 2783 2783 2783 R-squared 0.33 0.33 0.38 0.37 0.41 Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Extension 1: Headquarter Intensity

Theory predicts that:

◮ In complements case, ρ(1 − η) high, greater propensity to integrate

downstream when ρ is high and η is low

◮ In substitutes case, ρ(1 − η) low, greater propensity to outsource

downstream when ρ is low and η is high

◮ Suggests a triple interaction approach: further interaction with hq intensity

Use first principal component of log(s/l), log(equipment k/l), and log(R&D/Sales) as measure of headquarter intensity.

◮ Complements case: results indeed strongest in lowest quintile of η ◮ Substitutes case: results more noisy but broadly supportive

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Extension 1: Headquarter Intensity (cont.)

(1) (2) (3) (4) (5) (6) Downstreamness:

DUse_TUse DUse_TUse DUse_TUse DownMeasure DownMeasure DownMeasure

Buyer industry hq intensity:

Weighted Weighted Weighted Weighted

Downstream X 1 (Elas < Med) X (HQ Quintile 1) 0.049 0.009

• 0.016

0.351*** 0.301** 0.290** [0.129] [0.139] [0.118] [0.128] [0.134] [0.129] Downstream X 1 (Elas < Med) X (HQ Quintile 2)

• 0.268**
• 0.477***
• 0.331**
• 0.161
• 0.312*
• 0.169

[0.118] [0.162] [0.148] [0.103] [0.186] [0.150] Downstream X 1 (Elas < Med) X (HQ Quintile 3)

• 0.175
• 0.162
• 0.158

0.072

• 0.02
• 0.058

[0.148] [0.138] [0.124] [0.131] [0.160] [0.145] Downstream X 1 (Elas < Med) X (HQ Quintile 4)

• 0.377***
• 0.658***
• 0.455***
• 0.121
• 0.394**
• 0.280**

[0.134] [0.108] [0.069] [0.128] [0.172] [0.125] Downstream X 1 (Elas < Med) X (HQ Quintile 5) 0.177

• 0.046

0.024 0.229

• 0.181
• 0.05

[0.171] [0.192] [0.172] [0.157] [0.160] [0.158] Downstream X 1 (Elas > Med) X (HQ Quintile 1) 0.196 0.805** 0.798*** 0.465*** 0.624*** 0.593*** [0.248] [0.325] [0.278] [0.163] [0.113] [0.087] Downstream X 1 (Elas > Med) X (HQ Quintile 2)

• 0.037
• 0.099
• 0.180

0.032

• 0.001
• 0.061

[0.146] [0.181] [0.175] [0.130] [0.238] [0.189] Downstream X 1 (Elas > Med) X (HQ Quintile 3) 0.216* 0.172 0.027 0.358*** 0.357 0.099 [0.119] [0.207] [0.145] [0.135] [0.257] [0.199] Downstream X 1 (Elas > Med) X (HQ Quintile 4) 0.130 0.819** 0.427 0.280* 0.519 0.079 [0.161] [0.390] [0.341] [0.159] [0.427] [0.352] Downstream X 1 (Elas > Med) X (HQ Quintile 5) 0.183** 0.271* 0.162 0.179 0.274 0.225* [0.082] [0.144] [0.114] [0.117] [0.197] [0.117] Industry controls for: Buyer Buyer Buyer Buyer Buyer Buyer Main and double interaction effects? Yes Yes Yes Yes Yes Yes Year fixed effects? Yes Yes No Yes Yes No Country-Year fixed effects? No No Yes No No Yes Observations 2783 2783 207991 2783 2783 207991 R-squared 0.40 0.69 0.63 0.40 0.71 0.65 First Principal Component: Log (s/l), Log (equipment k/l), and Log (0.001+R&D/Sales) Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Extension 2: Firm Heterogeneity

◮ Highest propensity to integrate in the first quintile of downstreamness when

ρ < ρmed; and in the last quintile of downstreamness when ρ > ρmed

(1) (2) (3) (4) (5) (6) Downstreamness:

DUse_TUse DUse_TUse DUse_TUse DownMeasure DownMeasure DownMeasure Weighted Weighted Weighted Weighted

(Downstream Quin 1) X 1(Elas < Median) 0.101** 0.210*** 0.145*** 0.060 0.184*** 0.145** [0.045] [0.058] [0.045] [0.051] [0.067] [0.059] (Downstream Quin 2) X 1(Elas < Median) 0.041 0.131** 0.096*

• 0.005

0.062 0.019 [0.043] [0.062] [0.054] [0.045] [0.069] [0.055] (Downstream Quin 3) X 1(Elas < Median) 0.008 0.063 0.010

• 0.016

0.089 0.049 [0.046] [0.057] [0.046] [0.049] [0.076] [0.060] (Downstream Quin 4) X 1(Elas < Median)

• 0.047

0.092 0.047 0.024 0.064 0.032 [0.043] [0.065] [0.051] [0.045] [0.075] [0.058] (Downstream Quin 5) X 1(Elas < Median) 0.017 0.084 0.082 0.023 0.039 0.058 [0.042] [0.063] [0.053] [0.042] [0.081] [0.064] (Downstream Quin 2) X 1(Elas > Median) 0.021 0.031 0.016 0.013

• 0.054
• 0.068

[0.036] [0.067] [0.056] [0.039] [0.069] [0.052] (Downstream Quin 3) X 1(Elas > Median) 0.086** 0.150** 0.072 0.035 0.076 0.018 [0.044] [0.065] [0.052] [0.047] [0.069] [0.066] (Downstream Quin 4) X 1(Elas > Median) 0.030 0.086 0.017 0.073* 0.056 0.013 [0.048] [0.056] [0.050] [0.043] [0.072] [0.060] (Downstream Quin 5) X 1(Elas > Median) 0.181*** 0.352*** 0.257*** 0.171*** 0.380*** 0.300*** [0.048] [0.067] [0.062] [0.059] [0.085] [0.074] Industry controls for: Buyer Buyer Buyer Buyer Buyer Buyer Downstream quin and Elasticity dummies? Yes Yes Yes Yes Yes Yes Year fixed effects Yes Yes No Yes Yes No Country-Year fixed effects No No Yes No No Yes Observations 2783 2783 207991 2783 2783 207991 R-squared 0.35 0.63 0.61 0.33 0.67 0.63

Dependent variable: Intrafirm Import Share Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Selection into intrafirm trade (Heckman selection)

◮ Excluded variable in the second-stage: interaction of measure of country costs of

entry and R&D intensity of the selling industry

(1) (2) (3) (4) (5) (6) Downstreamness:

DUse_TUse DUse_TUse DUse_TUse DownMeasure DownMeasure DownMeasure Probit Weighted Weighted Probit Weighted Weighted

Downstream X 1(Elas < Median) 0.047

• 0.073
• 0.072

0.634**

• 0.020
• 0.011

[0.310] [0.074] [0.074] [0.317] [0.097] [0.088] Downstream X 1(Elas > Median) 0.274 0.310*** 0.314***

• 0.291

0.353*** 0.347*** [0.252] [0.106] [0.102] [0.246] [0.078] [0.084] 1(Elas > Median) 0.003

• 0.268***
• 0.268***

0.661***

• 0.244***
• 0.234***

[0.231] [0.075] [0.075] [0.233] [0.076] [0.073] Seller Log (0.001+ R&D/Sales)

• 0.028***
• 0.028***

X Country Entry Costs [0.007] [0.007] Seller Log (0.001+ R&D/Sales) 0.030 0.026 [0.045] [0.041] Inverse Mills Ratio

• 0.120
• 0.082

[0.250] [0.197] Industry controls for: Buyer Buyer Buyer Buyer Buyer Buyer Country-year fixed effects? Yes Yes Yes Yes Yes Yes Sample: Total imports >=0 Total imports > 0 Total imports > 0 Total imports >=0 Total imports > 0 Total imports > 0 Observations 462990 186029 186029 462990 186029 186029 R-squared

• 0.63

0.63

• 0.64

0.64 Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Plan of Talk

• 1. Motivation and Introduction
• 2. Setup of the Core Model
• 3. Key Predictions
• 4. Extensions
• 5. Empirical Evidence
• 6. Conclusion

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Concluding Remarks

◮ Developed a model of organizational decisions for a production function

with a continuum of sequential stages

◮ For each stage, firm’s make-or-buy decision depends on that stage’s

position in the value chain

◮ When stage inputs are sequential complements: Outsource upstream and

Integrate downstream

◮ When stage inputs are sequential substitutes: Integrate upstream and

Outsource downstream

◮ Intuition driven by how effort choices of upstream stage suppliers affect

effort levels downstream

◮ Can be readily embedded into existing global sourcing frameworks ◮ Evidence based on U.S. related-party trade shares is broadly consistent

with the model’s predictions

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

The Make-or-Buy Decision

Proof heuristic: For a given stage m, adopt the solution approach in Antr` as and Helpman (2004, 2008) and consider the hypothetical case in which β(m) can be chosen from the continuum of values in [0, 1] Let β∗(m) denote the unconstrained bargaining share that solves

∂ΠS ∂β(m) = 0

Consider the behavior of β∗(m) in the two cases

Return Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

The Make-or-Buy Decision: Sequential Complements

For ρ > α: Tend to choose βO upstream, βV downstream

m β(m) 1 1 Locus: Φ = 0 (ρ > α case) 1− α

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

The Make-or-Buy Decision: Sequential Substitutes

For ρ < α: Tend to choose βO downstream , βV upstream

m β(m) 1 1 Locus: Φ = 0 (ρ < α case) 1− α

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Extension 1: Headquarter Intensity

q = θ h η η 1 x(j) 1 − η α I(j)dj 1−η

α

(9)

◮ Headquarter services, h, are fully noncontractible ◮ Provided by the firm before stage 0 commences ◮ All stage suppliers take h as given when they decide on x(j) ◮ η ∈ (0, 1): intensity of headquarter services

Return Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Extension 1: Headquarter Intensity (cont.)

◮ With the same demand function as before, this yields:

r(m) = A1−ρθρ h η ρη (1 − η)− ˜

ρ

m x(j)αdj ˜

ρ α

◮ This turns out to behave like the core model, but with ρ replaced by

˜ ρ ≡ (1 − η)ρ

Proposition

In the presence of headquarter services provided by the firm, the results in Propositions 1 and 2 continue to hold except for the fact that: (i) the complements and substitutes cases are now defined by ˜ ρ ≡ (1 − η) ρ > α and ˜ ρ ≡ (1 − η) ρ < α, respectively, and (ii) the range of stages that are vertically integrated is now also (weakly) increasing in η.

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Extension 1: Headquarter Intensity (cont.)

Remarks:

◮ Part (ii) of the proposition implies that the propensity to integrate rises as

hq services become more important in production (η rises)

◮ Recovers the Antr`

as (2003) result, although the empirical implementation will call for a slight variation: If we interpret hq services as being capital- or R&D-intensive, then would expect the share of intrafirm trade for a given input to be increasing in the (average) capital or R&D intensity of industries that buy the input in question

◮ Also from part (i) of the proposition, note that the likelihood that we find

• urselves in the sequential complements case is lower the higher is

headquarter intensity

◮ This is an auxiliary prediction of the model that we will test Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Extension 2: Firm Heterogeneity

Introduce two new features:

• 1. Industry contains many other firms that differ only in their productivity, θ,

which is drawn from a Pareto distribution: G (θ) = 1 − (θ/θ)z for θ ≥ θ > 0

• 2. Each production stage m incurs fixed organizational costs. Specifically,

assume that: fV > fO Firm’s objective is thus to maximize revenues net of total fixed costs, 1

j=0 f (j)dj

Return Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Extension 2: Firm Heterogeneity (cont.)

m 

 1 mC* C mC

Complements Case m

1 mS* mS  S

 Substitutes Case

Firms integrating stage mC Firms outsourcing stage mC Firms integrating stage mS Firms outsourcing stage mS

Complements case (ρ > α):

◮ For each θ, there exists a cutoff stage mC(θ) such that all stages before

mC(θ) are outsourced, and all stages after are integrated

◮ mC(θ) is decreasing in θ

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Extension 2: Firm Heterogeneity (cont.)

m 

 1 mC* C mC

Complements Case m

1 mS* mS  S

 Substitutes Case

Firms integrating stage mC Firms outsourcing stage mC Firms integrating stage mS Firms outsourcing stage mS

Conversely, in the substitutes case (ρ < α):

◮ For each θ, there exists a cutoff stage mS(θ) such that all stages before

mS(θ) are integrated, and all stages after are outsourced

◮ mS(θ) is increasing in θ

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Extension 2: Firm Heterogeneity (cont.)

Importantly, this generates smooth predictions for how the intrafirm trade share varies with production line position:

Proposition

The share of firms integrating a particular stage m is weakly increasing in the downstreamness of that stage in the complements case (ρ > α), while it is decreasing in the downstreamness of the stage in the substitutes case (ρ < α). Furthermore, the share of firms integrating a particular stage m, is weakly increasing in the dispersion of productivity within the industry.

◮ This converts previous within-firm variation on the propensity to integrate

different stages into predictions regarding the relative prevalence of integration of an input with a particular level of downstreamness

◮ If fixed costs of integration are relatively high, only most downstream (in

complements case) or most upstream stages (in substitutes case) will be integrated

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Extension 3: Input and Supplier Heterogeneity

Relaxing the symmetry in the production function: q = θ 1 (ψ (j) x(j))α I(j)dj 1/α (10) In practice:

◮ Production stages can have different weights ◮ Stage suppliers could defer in their productivity levels

Separately, production costs for stage j, c(j), might depend on which country the stage is located in

Return Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Extension 3: Input and Supplier Heterogeneity (cont.)

This more general model can be solved using a similar heuristic:

Proposition

Suppose that technology allows for input heterogeneity as in (10) and that marginal costs of production of inputs are also heterogeneous and given by c (j) for j ∈ [0, 1]. Then the share of firms integrating a particular stage m is weakly increasing in the downstreamness of that stage in the complements case (ρ > α), while it is decreasing in the downstreamness of that stage in the substitutes case (ρ < α).

Pol Antr` as Davin Chor Organizing the Global Value Chain

Motivation and Introduction A Property Rights Model in a Sequential Production Setting Empirical Evidence Empirical specification Measuring downstreamness Production Line Position and the Boundaries of the Firm

Extension 3: Input and Supplier Heterogeneity (cont.)

Caveats:

◮ c(m) is in principle endogenous, it being a function of location choice ◮ Marginal incentives for the Firm to reduce the marginal cost of a given

stage are indeed generally affected by the index of the production stage m, but this dependence is complex and hinges on various aspects of the model in subtle ways

◮ Empirically: Control for country fixed effects, to ensure that effects of

downstreamness are not being estimated off cross-country variation in production costs. Also, run a two-stage Heckman procedure to correct for selection bias

Pol Antr` as Davin Chor Organizing the Global Value Chain